I live in Central Michigan and my mint gets good sun with some afternoon shade and for the last 2 years the majority of it has gotten brown edges. I have to work really hard to find good bits of it to pick and use. I was told last year it is a fungus and I need to start with 'new' mint. Well, that is all good and well but it is in my raspberry patch and that makes it a hard place to tackle :-). The raspberry patch produced the best berries last year in our 9years in residence so whatever it is in the mint has not affected the raspberries. Funny you were living up here and moved to Houston. I lived in Houston and moved up here ;-) I know this does not answer your question but at least you know you are not alone!
Farmgirl Sister #918
I would rather sit on a pumpkin and have it all to myself, than be crowded on a velvet cushion. -Henry David Thoreau-
I would make sure you are watering frequently- my mint loves it's water! If that doesn't stop more brown leaves from happening, pinch off the brown leaves as soon as you can since it might be that rust fungus.
My mint seems to have some problem - older plants have infestations - not sure if a parasite fungus or insect... I have to kill some of it. to get rid of the infestation.
The nice thing about mint is that it is hard to completely kill off. What comes back after you try to get rid of it are plants that have adapted to local conditions, hopefully!